The time complexities of bucket sort and RADIX sort are well known, but they vary depending on which variant of the sort is used. Normal bucket sort has time complexity of \(\Theta (n+r)\)  where r is the range of numbers [1]}. RADIX sort has a time complexity of \(\Theta (d(n+k))\)  [1]}, where \(d\)  is the number of digits in the largest integer and each digit can take \(k\)  values. The average time complexity is the same as the worst case for both algorithms.
